: In

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, the Morton number (Mo) is a

dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

used together with the

Eötvös number In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to surface tension forces for the movement of liquid front. Alongside the Capillary nu ...

or Bond number to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, ''c''. It is named after

Rose Morton Rose Katherine Morton-Sayre (December 3, 1925 – November 12, 1999) was an American mathematician known for her work in fluid mechanics. The Morton number, a dimensionless parameter used to describe bubbles, is named after her. Morton was b ...

, who described it with W. L. Haberman in 1953.

Definition

The Morton number is defined as :

\mathrm = \frac,

where ''g'' is the acceleration of gravity,

\mu_c

is the

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

of the surrounding fluid,

\rho_c

the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of the surrounding fluid,

\Delta \rho

the difference in density of the phases, and

\sigma

is the

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...

coefficient. For the case of a bubble with a negligible inner density the Morton number can be simplified to :

\mathrm = \frac.

Relation to other parameters

The Morton number can also be expressed by using a combination of the

Weber number The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named ...

Froude number In continuum mechanics, the Froude number (, after William Froude, ) is a dimensionless number defined as the ratio of the flow inertia to the external field (the latter in many applications simply due to gravity). The Froude number is based on t ...

and

Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...

, :

\mathrm = \frac.

The Froude number in the above expression is defined as :

\mathrm = \frac

where ''V'' is a reference velocity and ''d'' is the equivalent diameter of the drop or bubble.

References

{{NonDimFluMech Dimensionless numbers Bubbles (physics) Dimensionless numbers of fluid mechanics Fluid dynamics